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Logarithmic tensor category theory, VI: Expansion condition, associativity of logarithmic intertwining operators, and the associativity isomorphisms
Logarithmic tensor category theory, VI: Expansion condition associativity of logarithmic intertwining operators associativity isomorphisms
2011/2/23
This is the sixth part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (...
We prove explicit formulas for Chern classes of tensor products of vector bundles, with coefficients given by certain universal polynomials in the ranks of the two bundles.
Generalization of the Bollobás-Riordan polynomial for tensor graphs
(multivariate) topological graph polynomials group eld theory
2011/1/19
Tensor models are used nowadays for implementing a fundamental theory of quan-tum gravity. We de ne here a polynomial T encoding the supplementary topological information.
CMB Bispectrum from Primordial Scalar, Vector and Tensor non-Gaussianities
CMB Bispectrum Primordial Scalar Vector Tensor non-Gaussianities
2011/3/2
We present an all-sky formalism for the CMB bispectrum induced by the primordial non-Gaussianities not only in scalar but also in vector and tensor fluctuations. We find that the bispectrum can be for...
Logarithmic tensor category theory, III: Intertwining maps and tensor product bifunctors
Logarithmic tensor category theory Intertwining maps and tensor product bifunctors
2011/2/23
This is the third part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (...
Logarithmic tensor category theory, II: Logarithmic formal calculus and properties of logarithmic intertwining operators
Logarithmic tensor category theory Logarithmic formal calculus properties of logarithmic intertwining operators
2011/2/23
This is the second part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper ...
We examine the use of the mathematics of category theory in the description of quantum states
by tensor networks. This approach enables the development of a categorical framework allowing a
solution...
Logarithmic tensor category theory for generalized modules for a conformal vertex algebra, I: Introduction and strongly graded algebras and their generalized modules
Logarithmic tensor category theory for generalized modules conformal vertex algebra Introduction strongly graded algebras generalized modules
2011/2/23
This is the first part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra.
Quantum Geometric Tensor (Fubini-Study Metric) in Simple Quantum System: A pedagogical Introduction
Quantum Geometric Tensor Simple Quantum System pedagogical Introduction
2011/3/2
Geometric Quantum Mechanics is a novel and prospecting approach motivated by the belief that
our world is ultimately geometrical. At the heart of that is a quantity called Quantum Geometric Tensor (o...
Tensor products of representations up to homotopy
Tensor products of representations homotopy
2010/12/14
We study the construction of tensor products of representations up to homotopy, which
are the A∞ version of ordinary representations. We provide formulas for the construction
of tensor products of r...
Three-Colorings of Cubic Graphs and Tensor Operators
3-colorings of cubic planar graphs tensor algebras
2010/12/6
Penrose’s work [6] established a connection between the edge 3-colorings of cubic planar graphs and tensor algebras. We exploit this point of view in order to get algebraic representations of the cate...
Covering morphisms of crossed complexes and of cubical omega-groupoids with connection are closed under tensor product
Covering morphisms of crossed complexes omega-groupoids connection
2010/12/14
The aim is the theorems of the title and the corollary that the tensor product of two free crossed resolutions of groups or groupoids is also a free crossed resolution of the product group or groupoid...
Small Ball Probabilities for Smooth Gaussian fields and Tensor Products of Compact Operators
Small deviations slowly varying functions smooth covariances
2010/12/10
We find the logarithmic L2-small ball asymptotics for a class of zero mean Gaussian fields with covariances having the structure of “tensor product”. The main condition imposed on marginal covariances...
TransverseDiff gravity is to scalar-tensor as unimodular gravity is to General Relativity
TransverseDiff gravity scalar-tensor unimodular gravity General Relativity
2010/12/15
Transverse Diffeomorphism (TDiff) theories are well-motivated theories of gravity from the quantum perspective, which are based upon a gauge symmetry principle. The main contribution of this work is t...
On P-Sasakian Manifolds Satisfying Certain Conditions on the Concircular Curvature Tensor
P-Sasakian manifold concircular curvature tensor Weyl conformal curvature tensor
2010/2/26
We classify P-Sasakian manifolds, which satisfy the conditions Z(x ,X) · Z = 0, Z(x ,X) · R = 0, R(x ,X) · Z = 0, Z(x ,X) · S = 0 and Z(x ,X) · C = 0.